I haven't specifically asked someone to pray for me but in similar such instances -- when I've asked for something that's important to someone else but which I know little about -- it's usually been a way for me to make concrete whatever emotion feels too overwhelming to verbalize in that relationship.

As in, somehow to know / feel that there is something tangible by way of which I'm imprinted in the other person's memory / consciousness (for however short a while) has been comforting and given me a sense of security and safety.

And yeah, that would make me emotional because to me it's been a means of solidifying and holding on to a safe attachment given that my attachments in general have been tenuous, fleeting, scattered, inconsistent, unsafe etc.